2,421 research outputs found
An Algebraic Approach to Mso-Definability on Countable Linear Orderings
We develop an algebraic notion of recognizability for languages of words indexed by countable linear orderings. We prove that this notion is effectively equivalent to definability in monadic second-order (MSO) logic. We also provide three logical applications. First, we establish the first known collapse result for the quantifier alternation of MSO logic over countable linear orderings. Second, we solve an open problem posed by Gurevich and Rabinovich, concerning the MSO-definability of sets of rational numbers using the reals in the background. Third, we establish the MSO-definability of the set of yields induced by an MSO-definable set of trees, confirming a conjecture posed by Bruyère, Carton, and Sénizergues
What Makes a Computation Unconventional?
A coherent mathematical overview of computation and its generalisations is
described. This conceptual framework is sufficient to comfortably host a wide
range of contemporary thinking on embodied computation and its models.Comment: Based on an invited lecture for the 'Symposium on
Natural/Unconventional Computing and Its Philosophical Significance' at the
AISB/IACAP World Congress 2012, University of Birmingham, July 2-6, 201
The prospects for mathematical logic in the twenty-first century
The four authors present their speculations about the future developments of
mathematical logic in the twenty-first century. The areas of recursion theory,
proof theory and logic for computer science, model theory, and set theory are
discussed independently.Comment: Association for Symbolic Logi
Uniform Definability in Propositional Dependence Logic
Both propositional dependence logic and inquisitive logic are expressively
complete. As a consequence, every formula with intuitionistic disjunction or
intuitionistic implication can be translated equivalently into a formula in the
language of propositional dependence logic without these two connectives. We
show that although such a (non-compositional) translation exists, neither
intuitionistic disjunction nor intuitionistic implication is uniformly
definable in propositional dependence logic
Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent?
I argue that a criterion of theoretical equivalence due to Clark Glymour
[Nous 11(3), 227-251 (1977)] does not capture an important sense in which two
theories may be equivalent. I then motivate and state an alternative criterion
that does capture the sense of equivalence I have in mind. The principal claim
of the paper is that relative to this second criterion, the answer to the
question posed in the title is "yes", at least on one natural understanding of
Newtonian gravitation.Comment: 27 page
Deciding definability in FO2(<h,<v) on trees
We provide a decidable characterization of regular forest languages definable
in FO2(<h,<v). By FO2(<h,<v) we refer to the two variable fragment of first
order logic built from the descendant relation and the following sibling
relation. In terms of expressive power it corresponds to a fragment of the
navigational core of XPath that contains modalities for going up to some
ancestor, down to some descendant, left to some preceding sibling, and right to
some following sibling. We also show that our techniques can be applied to
other two variable first-order logics having exactly the same vertical
modalities as FO2(<h,<v) but having different horizontal modalities
Definability of groups in -stable metric structures
We prove that in a continuous -stable theory every type-definable
group is definable. The two main ingredients in the proof are:
\begin{enumerate} \item Results concerning Morley ranks (i.e., Cantor-Bendixson
ranks) from \cite{BenYaacov:TopometricSpacesAndPerturbations}, allowing us to
prove the theorem in case the metric is invariant under the group action; and
\item Results concerning the existence of translation-invariant definable
metrics on type-definable groups and the extension of partial definable metrics
to total ones. \end{enumerate
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